Introduction

I am blessed to have a cat baby, and I enjoy baking a lot, however recently I started to lose weight. So my amazon records looks like this:

• Months 1–6: lots of cat stuff (litter mat, fountain, scratching post, treats, toys, carrier).
• Months 7–9: baking accessories (sheet pans, silicone mats, piping bags, cake turntable, mixer bowl).
• Last 2 weeks: workout kick (Theragun → whey protein → lifting gloves).

Apparently my purchases have sequential dependencies, which are unable to be captured by conventional recommendation systems, including collaborative filtering and content-based filtering, as they model/depict consumers by their interaction to the items and it’s order-agnostic and it’s also just pair-wise correlation between the consumer and items based on engagements (clicks, conversions etc).

And to model such sequential dependencies, there are a lot of different models from non-DNN, DNN, to latest LLM. This doc summarizes how each model works for my user behaviors. For difficulties/challenges/characteristics of sequential recommender, please refer to Sequential Recommender Systems: Challenges, Progress and Prospects

Collaborative Filtering - Matrix-factorization CF

Matrix-Factorization CF learns a latent vector p_u for each user. Although it’s not frequency by category, but in practice, p_u ends up to be a function that normalizes the user factor by engagement with confidence scores.

The key components are:

• |I| is the size of items; k is item factor dimensions.
• Q: Item factor matrix, where each row is a k-dimensional vector for an item
• C_u: A diagonal confidence matrix of user u for items, where c_ui is the confidence score of user u with item i, normally derived from engagement data (clicks, conversions)

The confidence score is typically defined as:

c_ui = 1 + α * r_ui

Where r_ui is the interaction metric (clicks, conversions).

The normalization term ensures that the learned consumer representations are weighted by engagement (clicks/conversions) on item vectors. In the example, the user representation will be closest to cat supplies embeddings, so predictions will likely favor cat supplies.

Before DNN - Sequential pattern mining

Mine frequent patterns on sequence data, and then utilize the patterns for subsequent recommendations. Although simple and straightforward, but the patterns could be redundant. e.g. I am buying cat supplies monthly, while sometimes buying bake supplies in between. The pattern could be something like cat_food -> cat_litter -> baking_supplies.

Basic Markov Chain

The hypothesis is that future purchases depend only on the previous k purchases. A transition matrix is learned where each value represents how often transitions occur from state i to state j, with row normalization (each row sum = 1).

Key concepts:

• First order chain: Computes P(x_{t+1}=j | x_t = i)
• High order chain: Computes P(x_{t+1}=j | x_t, x_{t-1}, …, x_{t-k})
  • For high order chains, the predicted probability is: P(X,T) = P(x_1, …x_k) × ∏{t=k+1}^T P(x_t | x{t-1}…x_{t-k})

Transition matrix: The transaction matrix is computed as: T_ij = #(i → j) / ∑_{j’} #(i → j')

Since the last item is lifting glove, the prediction will be whichever item has the largest probability in the lifting glove row of the transition matrix.

Latent Markov Embedding based approach

Deep Learning Era

RNN-based approaches

Recurrent Neural Networks can capture longer-term dependencies in sequential data, making them more suitable for modeling complex user behavior patterns.

Attention-based models

Modern attention mechanisms can focus on relevant parts of the purchase history when making recommendations.

LLM Wave

Large Language Models for recommendation

Recent advances in LLMs show promise for understanding complex user preferences and generating personalized recommendations based on natural language descriptions of user behavior.

Conclusion

Sequential recommendation systems offer a more nuanced understanding of user behavior by considering the temporal order of interactions. While traditional methods focus on static user-item relationships, sequential models can capture evolving preferences and behavioral patterns over time.